The study of Fluid Structure Interaction (FSI) is becoming of great interest in many engineering applications. In this work we propose a new model to study the deformation of solid structures induced by a two-phase flow. We use a monolithic approach for the FSI problem while a Volume Of Fluid method (VOF) is considered for the reconstruction and advection of the interface. A PLIC method based on the ELVIRA algorithm for the reconstruction and a split algorithm for the interface advection is used. For an accurate reconstruction of the interface a huge number of computational elements are required and a multilevel algorithm coupled to an efficient compression-expansion technique is developed to reduce computational costs and memory requirements. An unstructured computational grid and a fine Cartesian mesh are used for the FSI and the VOF problem, respectively. The interaction between the two different grids is obtained by projecting the velocity field into the Cartesian grid and the Color function into the unstructured grid. This is performed with the MEDMEM libraries included in the Salome platform. The FSI problem is solved with a parallel multigrid C++ Finite Element code. Several test cases are presented.